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B. T-primes

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputWe know that prime numbers are positive integers that have exactly two distinct positive divisors. Similarly, we'll call a positive integer *t* Т-prime, if *t* has exactly three distinct positive divisors.

You are given an array of *n* positive integers. For each of them determine whether it is Т-prime or not.

Input

The first line contains a single positive integer, *n* (1 ≤ *n* ≤ 10^{5}), showing how many numbers are in the array. The next line contains *n* space-separated integers *x*_{i} (1 ≤ *x*_{i} ≤ 10^{12}).

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is advised to use the cin, cout streams or the %I64d specifier.

Output

Print *n* lines: the *i*-th line should contain "YES" (without the quotes), if number *x*_{i} is Т-prime, and "NO" (without the quotes), if it isn't.

Examples

Input

3

4 5 6

Output

YES

NO

NO

Note

The given test has three numbers. The first number 4 has exactly three divisors — 1, 2 and 4, thus the answer for this number is "YES". The second number 5 has two divisors (1 and 5), and the third number 6 has four divisors (1, 2, 3, 6), hence the answer for them is "NO".

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